Welcome to QSER’s documentation!

QSER is a Data Physics tool for forward and inverse modeling and forecasting of physical systems.

Authors: Ahmad Muhammad and Fatih Külahcı

Version: 1.0.0

License: MIT

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Quick Start

### Installation

pip install QSER

### 1D Mesh and Gradient

import QSER as qs
import numpy as np
import matplotlib.pyplot as plt

# Create mesh
mesh = qs.Mesh.Structured1D(nx=100, L=10.0)
x = mesh.get_cell_centers()

# Create field
field = np.sin(x)

# Compute gradient
from QSER.Operators import Gradient
grad = Gradient(backend='numpy', method='5point')
df_dx = grad.compute(field, dx=x[1]-x[0])

# Plot
plt.plot(x, field, label='sin(x)')
plt.plot(x, df_dx, label='cos(x) (numerical)')
plt.legend()
plt.show()

### Energy Tracking

from QSER.Energy import EnergyTracker

tracker = EnergyTracker(backend='numpy')
eps_S = tracker.epsilon_S(S_field)
eps_E = tracker.epsilon_E(E_field)
eps_R = tracker.epsilon_R(R_field)

print(f"Source Energy: {eps_S:.6f}")
print(f"Environment Energy: {eps_E:.6f}")
print(f"Response Energy: {eps_R:.6f}")

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Core Concepts

The QSER framework is built on four fundamental equations:

\[R = S - E\]
\[L = L_c + L_d\]
\[L_c S = F\]
\[L E = L_d S\]

Where:

  • R = Response (observed field)

  • S = Source (conservative ghost field)

  • E = Environment (memory accumulator)

  • Q = Memory (Green’s function)

  • L_c = Conservative operator

  • L_d = Dissipative operator

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Features

  • Mesh & Geometry — Structured 1D/2D/3D meshes + STL/CAD geometry import

  • Operators — Gradient, Laplacian, Divergence, Curl, TimeGradient

  • Backends — NumPy, PyTorch, JAX, OpenFOAM

  • Energy Tracking — ε_S, ε_E, ε_R, J_SE, D_E

  • QSER Decomposition — R = S - E, L = Lc + Ld

  • Integration Engine — Trapezoidal, Simpson, Monte Carlo, Quasi-Monte Carlo

  • Boundary Conditions — Dirichlet, Neumann, Robin, Periodic, Wall, Source

  • Physics-Informed Neural Networks (PINNs) — Mesh-free and mesh-based

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Citation

If you use QSER in your research, please cite:

@software{muhammad2026qser,
  author = {Muhammad, Ahmad and K\"ulahc{\i}, Fatih},
  title = {QSER: A Data Physics Framework for Forward and Inverse Modeling of Physical Systems},
  year = {2026},
  url = {https://github.com/1030ahmad1030/QSER},
  version = {1.0.0},
  doi = {10.5281/zenodo.21965738}
}

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Indices and tables